title: Intermittency in relation with 1/f noise and stochastic differential equations.
abstract: One of the models of intermittency is on-off intermittency, arising due to time-dependent forcing of a bifurcation parameter through a bifurcation point. For on-off intermittency, the power spectral density (PSD) of the time-dependent deviation from the invariant subspace in a low frequency region exhibits 1/√f power-law noise. Here, we investigate a mechanism of intermittency, similar to the on-off intermittency, occurring in nonlinear dynamical systems with invariant subspace. In contrast to the on-off intermittency, we consider the case where the transverse Lyapunov exponent is zero. We show that for such nonlinear dynamical systems, the power spectral density of the deviation from the invariant subspace can have 1/f(β) form in a wide range of frequencies. That is, such nonlinear systems exhibit 1/f noise. The connection with the stochastic differential equations generating 1/f(β) noise is established and analyzed, as well.
authors.affiliation: Institute of Theoretical Physics and Astronomy, Vilnius University, A. Goštauto 12, LT-01108 Vilnius, Lithuania. julius.ruseckas@tfai.vu.lt
authors.forename: J
authors.initials: J
authors.lastname: Ruseckas
authors.forename: B
authors.initials: B
authors.lastname: Kaulakys